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In triangle XYZ, we have angle X = 90 and tan Y = 3/2. If YZ = 80, then what is XY?

 May 6, 2022
 #1
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Y

 

 

X        Z

 

tan Y  =  XZ / XY =   3/2   ⇒   XZ =  (3/2)XY

 

Therefore, by Pythagoras

 

XY^2  + XZ^2  = 80^2

 

XY^2  +  [ (3/2) XY ] ^2  =  6400

 

XY^2  + (9/4)XY^2  = 6400

 

(13/4)XY^2  = 6400

 

XY^2 =  6400 / (13/4)

 

XY^2  = 6400 * 4  / 13

 

XY  =   sqrt [   (6400 * 4 )  / 13  ]  =   160  / sqrt 13  ≈  44.38

 

cool cool cool

 May 6, 2022

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